Description: In a product warranty, the renewal function is the expected number of failures in a specific warranty duration. To estimate the renewal function, cross-sectional regression data is assumed to be available and the data is assumed to be semiparametric. In this article, the observations are a11owed to be residuals from a complex regression model. It is observed that estimation can be accomplished using reasonable models for the contracts and data collection. From Actuarial Research Clearing House 1992, VOL. 2.

Description: Automobile insurers classify the risks that they underwrite in order to subdivide the portfolio into classes of risks with similar profiles. While some insurers may have sufficient historical data, several others may not have significant volume of experience data in order to produce reliable claims predictions to help enhance their risk classification systems. A database containing a pooled experience of several insurers thereby helps to produce a more fair, reliable, and equitable premium structure for all risks concerned. This paper uses multilevel models to analyze the data on claim counts provided by the General Insurance Association of Singapore, an organization consisting of most of the general insurers in Singapore. The multilevel nature of the data is due to the following: a certain vehicle is observed over a period of years and is insured by a particular insurance company under a certain 'fleet' policy. The authors show how intercompany data lead to a priori premiums and a posteriori corrections to these initial premiums. Specific focus is made in understanding the intercompany effects using various count distribution models [Poisson, negative binomial, zero–inflated and hurdle Poisson]. The performance of these various models is compared the authors also investigate how to use the historical claims of a company, fleet and/or vehicle in order to correct for the premium initially set.

Description: This article discusses Jed Frees’ book in progress, “Regression Modeling with Actuarial and Financial Applications” which offers a synthesized introduction to regression and time series.

Description: This paper introduces actuaries to the concept of 'copulas,' a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Recently, there has been a rapidly developing literature on the statistical properties and applications of copulas. This paper explores some of these practical applications, including estimation of joint life mortality and multidecrement models. In addition, the paper describes basic properties of copulas, their relationships to measures of dependence and several families of copulas that have appeared in the literature. This paper will also be useful to those who wish to use copulas for statistical inference. Statistical inference procedures are illustrated using insurance company data on losses and expenses. For this data, the paper shows how to fit copulas and describes their usefulness by pricing a reinsurance contract and estimating expenses for pre-specified losses.

Description: This paper introduces density estimation for functions of observations. The nonparametric density estimates are introduced and certain computational issues are discussed and a central limit theorem for the estimator is provided. From Actuarial Research Clearing House 1993, VOL. 1.

Description: The purpose of this paper is to understand characteristics of a household that drive life insurance demand with more sophisticated analytical techniques. The analysis is based on the Survey of Consumer Finances data, a probability sample of the U.S. population. Household demand of two types of insurance, term life insurance and whole life insurance, is examined jointly. We model both the frequency and the severity of demand for insurance building on the work of Lin and Grace 2007 by using covariates that they developed.

Description: Abstract for a paper that develops links between credibility theory in actuarial science and longitudinal data models in statistics. The paper demonstrates that many additive credibility models can be expressed as special cases of the longitudinal data model.